With organ donors most are in types of situations where they have suffered a great deal of brain injury or are otherwise in a sort of "coma" like state. And the organs are taken while the person is basically unconscious but pretty close to death (never full body death, but brain death). If the donor had a lot of hospitalizations or are sickly beforehand they don't usually accept the organs. There is a time issue in these cases and there is a lot stuff that has to be done fast, but again these cases are usually "brain death" so it's not like the donor is going to have any chance of consciousness during. http://organdonor.gov/about/organdonationprocess.html